Radial stiffness analysis of circular ring with uncertain boundary conditions: Mechanical elastic wheel as an example

The paper studies the radial stiffness of mechanical elastic wheel (MEW), which is regarded as a circular ring with uncertain boundary conditions for the first time, and proposes a ring-chain model to solve the radial stiffness of the ring. Different from assuming the boundary conditions by experience or building finite element model with complex processes from previous researches, the ring-chain model coupling circular ring model and dynamics of multi-rigid body is accurate and simple to find the loaded positions of ring and make the boundary conditions clear. The results show that the ring-chain model can be solved to get the deformations and loaded positions of ring, the radial stiffness of MEW is large, and the radial displacement of MEW increases non-linearly. The results are consistent with that from finite element model under the same settings, but the time cost of ring-chain model is less. In addition, the influence factors of ring radial stiffness are also found and analyzed. The method presented in this paper can provide data for the response analyses of vehicle and references for the analysis of circular ring with uncertain boundary conditions.

Using wavelets to verify the scale structure of precipitation forecasts

Recently developed verification tools based on local wavelet spectra can isolate errors in the spatial structure of quantitative precipitation forecasts, thereby answering the question of whether the predicted rainfall variability is distributed correctly across a range of spatial scales. This study applies the wavelet-based structure scores to real numerical weather predictions and radar-derived observations for the first time. After tackling important practical concerns such as uncertain boundary conditions and missing data, the behaviour of the scores under realistic conditions is tested in selected case studies and analysed systematically across a large data set. Among the two tested wavelet scores, the approach based on the so-called map of central scales emerges as a particularly convenient and useful tool: summarizing the local spectrum at each pixel by its centre of mass results in a compact and informative visualization of the entire wavelet analysis. The histogram of these scales leads to a structure score which is straightforward to interpret and insensitive to free parameters like wavelet choice and boundary conditions. Its judgement is largely the same as that of the alternative approach (based on the spatial mean wavelet spectrum) and broadly consistent with other, established structural scores.